An arrangement and a method in differential phase-contrast computed tomography (DPC-CT) using X-ray radiation is able to not only illustrate the three-dimensional or layered distribution of the attenuation coefficient μ(x,y,z), but can also reconstruct the refractive index n=1−δ(x,y,z) from the measured data. In order to achieve this, the angle of refraction, that is to say a small deflection of the X-ray radiation when passing through an object, is also measured in a spatially resolved fashion in the projections in addition to the intensity of the transmitted X-ray radiation. In order to measure this angle of refraction, use is made of the design of a Talbot interferometer, possibly with the additional use of a source grid. In respect of such an arrangement and such a method, reference is made in an exemplary fashion to the documents DE 10 2006 037 255 A1, DE 10 2006 017 291 A1 and DE 10 2006 015 356 A1.
However, these known arrangements and methods only measure one component of the angle of refraction, that is to say the angle in the plane spanned by the beam direction and the normal of the grid structure, using the one-dimensional phase grids described therein. Accordingly, phase information at an angle to the plane spanned by the beam direction and the normal of the grid structure is only reproduced in a reduced fashion or not at all.